The present invention is related to the subject matter of our copending U.S. patent application Ser. No. 221,956, filed Dec. 31, 1980, for Controlling light. Said application is assigned to the assignee of the present invention. To the extent that any subject matter disclosed or claimed in the present application may be considered to be disclosed in, or obvious from, our copending earlier application cited above, the benefit of the filing date of the earlier application is hereby claimed for such subject matter under 35 USC 120. Also said application is hereby incorporated hereinto by reference and made a part hereof the same as if fully set forth herein.
The electrooptic components employed in typical embodiments of the present invention are now well known. Convenient ways of making them are described in the above mentioned patent application and in the references cited therein.
Apparatus according to the present invention typically comprises an electrooptic waveguide upon which is placed a double array of interdigital electrodes similar to the ones shown in the drawings. When any element of this array is actuated by the application of a voltage relative to the center electrode, a phase grating is induced into the waveguide underneath that can efficiently diffract light incident upon it at the correct (Bragg) angle. If the left half of the array is actuated with voltages V.sub.1,V.sub.2, . . . , and the corresponding elements of the array are actuated with voltages V.sub.1 ',V.sub.2 ', . . . , then light diffracted from the left half of an array element will be rediffracted from the right half of the element. The twice-diffracted light has intensity given by EQU I.sub.j =.eta..sub.j .eta..sub.j '.multidot.I.sub.O
for the j-th element, where I.sub.O is the incident intensity, and .eta..sub.j, .eta..sub.j 'are the efficiencies of the gratings induced by V.sub.j and V.sub.j ', respectively. The efficiency of an induced grating is EQU .eta.=sin.sup.2 (.alpha.V)
where .alpha. is a constant, independent of V, and V is the applied voltage. For small signals, the twice-diffracted beam from element j will have intensity proportional to V.sub.j.sup.2 .multidot.v.sub.j '.sup.2, so summing over j will give an intensity proportional to the vector product P.multidot.P', the vectors whose components are power stored on the array elements (power stored=CV.sup.2 /2 where C is the capacitance of the element). If the electrodes are biased to the inflection point of the grating response curve (efficiency-vs-voltage), then the small-signal from an element will be a linear function of the product of the voltages. In this case, the output beam will have a recoverable part whose intensity is proportional to the product of the voltages, and their summation will have a part proportional to the vector product V.multidot.V', where the components are the voltages. This may be a more useful application.
Other typical apparatus according to the invention comprises an arrangement for utilizing an electrooptic vector multiplying element to generate the product of a matrix times a vector. If the matrix is written as the array of its row vectors, ##EQU1## then the device generates ##EQU2## The arrangement produces the terms in the expansion in a unique way by generating .nu. once, then replicating N times, thus reducing the number of connections needed from 2N.sup.2 +1 to N.sup.2 +N1 a reduction of N.sup.2 -N. The indicated summation is performed by a lens.
Typical apparatus according to the present invention for receiving light entering in a predetermined input direction therein and controlling the directions in which portions of the light travel through regions thereof so as to emerge therefrom in a selected output direction with intensity responsive to the product of a plurality of electrical potential differences multiplied together, comprises an electrooptic waveguide, first electrooptic reflective means, comprising a first electrode and a second electrode, on a first region in the waveguide, for forming a first Bragg grating in the first region positioned with a direction of Bragg incidence approximately in the predetermined input direction, intermediate means for directing light reflected from the first Bragg grating in a predetermined intermediate direction into a second region in the waveguide, second electrooptic reflective means, comprising a third electrode and a fourth electrode, on the second region in the waveguide, for forming a second Bragg grating in the second region positioned with a direction of Bragg incidence in approximately the predetermined intermediate direction, light input means for directing light of known controlled intensity to enter approximately in the predetermined input direction into the first electrooptic means, first control means for applying a first electrical potential to the first electrode and a second electrical potential to the second electrode, to further direct a portion of the light entering into the first region by providing a first Bragg reflection thereof into the intermediate means, and second control means for applying a third electrical potential to the third electrode and a fourth electrical potential to the fourth electrode, to further direct a portion of the light reflected into the second region by providing a second Bragg reflection thereof beyond the second region in the selected output direction.
Where the predetermined intermediate direction is approximately the same as a direction of Bragg reflection from the first Bragg grating, the intermediate means typically comprises means (which may be merely a portion of the waveguide) for transmitting light reflected from the first Bragg grating further in approximately the same direction into the second region in the waveguide.
Where the predetermined intermediate direction is different from any direction of Bragg reflection from the first Bragg grating, the intermediate means typically comprises means for changing the direction of light reflected from the first Bragg grating and directing it in approximately the predetermined intermediate direction into the second region of the waveguide.
Typical combination apparatus according to the invention may comprise a plurality of individual such apparatuses, each arranged adjacent to and in tandem with another.
The apparatus comprises also output means for receiving the twice-reflected light travelling beyond the second region in the selected output direction and for responding thereto.
In some typical embodiments of the invention the first control means comprises means for providing a fixed component of potential difference between the first and second electrodes such as to bias them to a value where the grating response is approximately a linear function of potential difference within a known range, and a variable component of potential difference within the range of the approximately linear response function; and the second control means comprises means for providing a fixed component of potential difference between the third and fourth electrodes such as to bias them to a value where the grating response is approximately a linear function of potential difference within a known range, and a variable component of potential difference within the range of the approximately linear response function; whereby the intensity of the light emerging in the selected output direction includes a part that is approximately a linear function of the product of the variable component of potential difference provided by the first control means multiplied by the variable component of potential difference provided by the second control means.
Some such embodiments typically comprise also means for providing an electric signal of amplitude responsive to the intensity of the light emerging in the selected output direction, and means for removing substantially all alternating components from the signal and thus leaving only direct components, which comprise approximately a linear function of the product of the variable component of potential difference provided by the first control means multiplied by the variable component of potential difference provided by the second control means.
Other such embodiments typically comprise also means for providing an electric signal of amplitude responsive to the intensity of the light emerging in the selected output direction, and means for removing substantially all components from the signal except the second harmonic alternating component, which comprises approximately a linear function of the product of the variable component of potential differences provided by the first control means multiplied by the variable component of potential difference provided by the second control means.
In typical embodiments of the invention for use in digital data processing equipment, the first control means comprises means for providing selectively either approximately zero potential difference or at least approximately a predetermined finite potential difference between the first and second electrodes, and the second control means comprises means for providing selectively either approximately zero potential difference or at least approximately a predetermined finite potential difference between the third and fourth electrodes; whereby the intensity of the light emerging in the selected output direction at a given instant is either approximately zero or at least approximately a determinable output value, as a digital binary AND function of the potential differences provided by the first and second control means.
Typical combination analog processing apparatus according to the invention comprises a plurality of individual such apparatuses, each arranged adjacent to and in tandem with another, wherein each first control means for providing a potential difference within a range wherein the grating response is approximately a quadratic function of potential difference, and each second control means comprises means for providing a potential difference within a range wherein the grating response is approximately a quadratic function of potential difference.
Such apparatus typically comprises also output means for receiving the twice-reflected light travelling beyond each second region in the selected output direction and directing substantially all of it to means for providing an electric signal of amplitude responsive to the intensity of the light and thus providing an indication responsive to the vector inner product of the squares of the potential differences on the individual first control means and the squares of the potential differences on the respective individual second control means.
Other typical, and generally preferred, apparatus according to the invention comprises, in combination, a plurality of individual such apparatuses, each operating within the range of its approximately linear response function and arranged adjacent to and in tandem with another, and output means for receiving the twice-reflected light travelling beyond each second region in the selected output direction and directing substantially all of it to means for providing an electric signal of amplitude responsive to the intensity of the light and thus providing an indication responsive to the vector inner product of the variable components of the potential differences on the individual first control means and the variable components of the potential differences on the respective individual second control means. In such apparatus, the output means typically comprises means for imaging the output light from the individual apparatuses onto photoelectric means.
Typical further combined apparatus according to the invention comprises a plurality of such combinations of individual apparatuses, wherein
individual potential differences comprising analogs of the individual component values of a selected vector are connected to the same respective first electrooptic reflective means in each such combination of individual apparatuses, and
individual potential differences comprising analogs of the individual values in each row of a selected matrix are connected to the same respective second electrooptic reflective means in one such combination, the potential differences for each row of the matrix being connected to a different combination of individual apparatuses from any combination to which the potential differences for any other row are connected,
whereby the output of each separate combination of individual apparatuses is an analog of one component value of the vector product of the selected matrix and the selected vector.
Other typical, and generally preferred, further combined apparatus for use in matrix by vector multiplication comprises
a plurality of individual first electrooptic reflective means, each arranged adjacent to and in tandem with another;
a like plurality of individual first control means, one for each individual first electrooptic reflective means;
a first like plurality of individual second electrooptic reflective means, one for each first electrooptic reflective means, each arranged adjacent to and in tandem with another, to form a first combination of individual second electrooptic reflective means;
a first like plurality of individual second control means, one for each individual second electrooptic reflective means in the first combination thereof, to form a first set of individual second control means;
at least one additional like combination of individual second electrooptic reflective means;
an additional like set of individual second control means for each additional combination of individual second electrooptic reflective means;
a plurality of intermediate means, one for each combination of individual second electrooptic reflective means, for directing light reflected from each first Bragg grating in the plurality of first electrooptic reflective means in approximately equal portions to the corresponding second Bragg grating in each combination of individual second electrooptic reflective means; and
a plurality of output means, one for each combination of individual second electrooptic reflective means;
each output means comprising means for receiving the light travelling beyond each second electrooptic reflective means in the selected output direction and directing substantially all of it to means for providing an electric signal of amplitude responsive to the intensity of the light and thus providing an indication that is an analog of one component value of the vector product of a matrix and a vector; where the potential differences provided by the individual first control means comprise analogs of the individual component values of the vector, the potential differences provided by the individual second control means of the first set thereof comprise analogs of the individual values in the first row of the matrix, and the potential differences provided by the individual second control means of each additional set thereof comprise analogs of the individual values in each respective succeeding row of the matrix,